Method for calculating potential of intermediate node of ferroelectric transistor

Abstract

The invention discloses a method for calculating the potential of an intermediate node of a ferroelectric transistor. The method comprises the following steps: according to a charge conservation relationship between a gate oxide layer and a semiconductor part in the ferroelectric transistor, determining a first function relationship between an intermediate node potential and a channel average surface potential under the condition of averaging a channel potential; determining a second function relationship among the average surface potential of the channel, the potential of the intermediate node, the voltage of the grid electrode, the voltage of the source electrode, the voltage of the drain electrode, the ferroelectric polarization state and the defect occupancy state by combining the charge conservation relationship of the ferroelectric layer; and on the basis of the second function relationship and by utilizing the first function relationship elimination, calculating the channel average surface potential and the intermediate node potential. According to the application, the potential of the middle node of the ferroelectric transistor can be quickly and accurately calculated, so that the direct-current conduction current of the channel of the ferroelectric transistor can be quickly calculated.

Description

Technical Field

[0001] This application belongs to the field of semiconductor technology, and in particular relates to a method for calculating the potential of the intermediate node of a ferroelectric transistor. Background Technology

[0002] A metal-ferroelectric-semiconductor FET (FeFET) is a memory device that integrates ferroelectric materials into the gate stack of a field-effect transistor. FeFETs store information by changing the threshold state of the ferroelectric material in the gate stack, thereby altering the threshold state. Compared to embedded flash memory, FeFETs offer advantages such as simpler cell structure, lower write power consumption, non-destructive readout, and CMOS process compatibility. Large-scale FeFET circuit design requires a compact model that can accurately and efficiently describe the dynamic electrical characteristics of FeFETs.

[0003] Currently, traditional model solution methods typically require binary search iterations of the potential between the ferroelectric layer and the interface layer, resulting in significant computational overhead. The traditional polycrystalline Monte Carlo NLS model introduces high computational complexity when describing the ferroelectric layer. Traditional models struggle to efficiently incorporate a model of defect-trapped charges, which is crucial for the dynamic characteristics of FeFETs.

[0004] Therefore, the current FeFET compact model suffers from the problem of not being able to balance computational efficiency and computational accuracy. Summary of the Invention

[0005] This application provides a method for calculating the intermediate node potential of a ferroelectric transistor, which can quickly and accurately calculate the intermediate node potential of the ferroelectric transistor, thereby facilitating the rapid calculation of the channel DC conduction current of the ferroelectric transistor.

[0006] On one hand, embodiments of this application provide a method for calculating the potential of an intermediate node in a ferroelectric transistor, including: Based on the charge conservation relationship between the gate oxide layer and the semiconductor portion in a ferroelectric transistor, and after averaging the channel potential, the first functional relationship between the intermediate node potential and the average surface potential of the channel is determined. By combining the ferroelectric layer charge conservation, a second functional relationship between the channel average surface potential and the gate voltage, source voltage, drain voltage, ferroelectric polarization state, and defect occupancy state is determined. The intermediate node potential is calculated based on the first functional relationship and the average surface potential of the channel.

[0007] In some embodiments, after calculating the intermediate node potential based on the first functional relationship and the channel average surface potential, the method further includes: Calculate the source-end surface potential and the drain-end surface potential based on the intermediate node potential, the source voltage, and the drain voltage; The channel DC conduction current is calculated based on the intermediate node potential, the source end surface potential, and the drain end surface potential.

[0008] In some embodiments, based on the charge conservation relationship between the gate oxide layer and the semiconductor portion in the ferroelectric transistor, and after averaging the channel potential, a first functional relationship between the intermediate node potential and the average surface potential of the channel is determined, including: Based on the charge conservation relationship between the gate oxide layer and the semiconductor part in the ferroelectric transistor, the third function relationship between the intermediate node potential and the channel surface potential is determined. The average channel potential is determined based on the source voltage and the effective drain voltage; wherein the effective drain voltage is determined based on the source voltage, drain voltage, and saturated drain voltage, and the saturated drain voltage is determined based on the gate voltage, source voltage, transistor threshold voltage, and transistor body effect coefficient. The fourth functional relationship between the average surface potential of the channel and the channel charge is determined based on ferroelectric materials and the average channel potential. The first functional relationship is determined based on the third functional relationship and the fourth functional relationship.

[0009] In some embodiments, the average channel potential is expressed as: ,in, The channel average potential, Source voltage, For effective drain voltage, ;in, Drain voltage This is the saturation drain voltage. ;in, Gate voltage, is the transistor threshold voltage, and m is the transistor bulk effect coefficient; The first functional relationship is expressed as: ,in, The potential at the intermediate node. It is a flat band voltage. The average surface potential of the channel is... For the channel potential, To determine the relationship between channel charge and channel surface potential based on ferroelectric materials. This refers to the capacitance per unit area of ​​the interface layer. This refers to the amount of defect charge injected into the interface layer.

[0010] In some embodiments, determining the second functional relationship between the channel average surface potential and the gate voltage, source voltage, drain voltage, and ferroelectric polarization state based on the first functional relationship includes: Based on the first functional relationship, the first expression for the metal gate charge, the second expression for the metal gate charge, and the third expression for the transistor equivalent charge, the second functional relationship is constructed. In the process of constructing the second functional relationship, based on the first functional relationship, the channel average surface potential is used to express the intermediate node potential so that there is no intermediate node potential in the constructed second functional relationship. Wherein, the first expression is the charge conservation relationship between the metal gate charge and the ferroelectric polarization state, gate voltage, and intermediate node potential; the second expression is the charge conservation relationship between the metal gate charge and the transistor equivalent charge and the intermediate metal layer charge; and the third expression is the charge conservation relationship between the transistor equivalent charge and the intermediate node potential, flat band voltage, and channel average surface potential.

[0011] In some embodiments, the first expression is , The second expression is , The third expression is , Among them, the This refers to the charge on the metal gate. It is in the ferropolar polarization state. Gate voltage, The potential at the intermediate node. The capacitance per unit area of ​​the ferroelectric layer. This is the equivalent charge of the transistor. The charge is that of the intermediate metal layer. It is a flat band voltage. The average surface potential of the channel is... This refers to the capacitance per unit area of ​​the interface layer. The step of constructing the second functional relationship based on the first functional relationship, the first expression for the metal gate charge, the second expression for the metal gate charge, and the third expression for the transistor equivalent charge includes: Substitute the first functional relationship into the first expression to obtain the fourth expression; Substituting the first functional relationship into the third expression, we obtain the fifth expression; Substitute the fourth and fifth expressions into the second expression to obtain the second functional relationship; The second functional relationship is: ,in, This refers to the amount of defect charge injected into the interface layer.

[0012] In some embodiments, the gate voltage, the source voltage, and the drain voltage are timing data. After calculating the channel DC conduction current based on the intermediate node potential, the source end surface potential, and the drain end surface potential, the method further includes: The magnitude of the ferroelectric layer field at time i is calculated based on the gate voltage and the intermediate node potential at time i; where time i is any time point in the timing sequence. Calculate the ferroelectric polarization state at time i+1 based on the magnitude of the ferroelectric layer field at time i. Based on the ferroelectric polarization state at time i+1, and assuming that the defects with trap energy levels are spatially uniformly distributed in the interface, calculate the defect charge at time i+1. Calculate the channel DC conduction current at time i+1 based on the gate voltage, source voltage, drain voltage, and defect charge at time i+1.

[0013] In some embodiments, calculating the ferroelectric polarization state at time i+1 based on the magnitude of the ferroelectric layer field at time i includes: The polarization reversal time constant is calculated based on the ferroelectric field magnitude at time point i, which is the distribution coefficient of the ferroelectric activation energy. ; Based on the polarization reversal time constant The ferropolarization state at time point i+1 is calculated using a preset time function; the preset time function decays exponentially from 1 to 0 as time increases.

[0014] In some embodiments, the preset time function is represented as: ,in, The attenuation coefficient is... It is a natural exponential function. For a point in time, The polarization reversal time constant. This is a preset constant.

[0015] In some embodiments, calculating the defect charge at time i+1, based on the ferroelectric polarization state at time i+1, when defects with trap energy levels are spatially uniformly distributed in the interface, includes: Based on the magnitude of the ferroelectric layer field at time point i, and assuming that defects with trap energy levels are spatially uniformly distributed in the interface, the relative energy difference between the channel conduction band and the defect energy level is calculated. Calculate the charge / discharge barrier based on the relative energy difference; Based on the band shift between the interface layer and the channel and the charge / discharge barrier, the tunneling probability is calculated when the defect with trap energy level is spatially uniformly distributed in the interface. The transition rate between occupied and unoccupied states of a defect with a trap energy level is calculated based on the tunneling probability. Based on the probability that a defect with a trap energy level is in an occupied state at time i, the conversion rate, and the unit time length, calculate the probability that a defect with a trap energy level is in an occupied state at time i+1. Calculate the defect charge at time i+1 based on the probability that a defect with a trap energy level is in an occupied state at time i+1.

[0016] On the other hand, embodiments of this application provide a device for calculating the intermediate node potential of a ferroelectric transistor, comprising: The first determining module is used to determine the first functional relationship between the intermediate node potential and the average surface potential of the channel, based on the charge conservation relationship between the gate oxide layer and the semiconductor part in the ferroelectric transistor and after averaging the channel potential. The second determining module is used to determine a second functional relationship between the channel average surface potential and the gate voltage, source voltage, drain voltage and ferroelectric polarization state based on the first functional relationship. The first calculation module is used to calculate the average surface potential of the channel based on the second functional relationship, according to the gate voltage, source voltage, drain voltage and ferroelectric polarization state. The second calculation module is used to calculate the intermediate node potential based on the first functional relationship and the average surface potential φ of the channel.

[0017] In another aspect, embodiments of this application provide an electronic device, which includes a processor and a memory storing computer program instructions. The processor reads and executes the computer program instructions stored in the memory to implement the method for calculating the intermediate node potential of the ferroelectric transistor described above.

[0018] In another aspect, embodiments of this application provide a computer-readable storage medium storing computer program instructions; when executed by a processor, the computer program instructions implement the method for calculating the intermediate node potential of the ferroelectric transistor as described above.

[0019] In another aspect, embodiments of this application provide a computer program product, including a computer program that, when executed, implements the method for calculating the intermediate node potential of the ferroelectric transistor as described above.

[0020] The method for calculating the intermediate node potential of a ferroelectric transistor according to embodiments of this application averages the channel potential and determines a first functional relationship between the intermediate node potential and the average surface potential of the channel based on the charge conservation relationship between the gate oxide layer and the semiconductor portion in the ferroelectric transistor. Then, based on the first functional relationship, the intermediate node potential is eliminated, and a second functional relationship between the average surface potential of the channel and the gate voltage, source voltage, drain voltage, and ferroelectric polarization state is determined. Based on the second functional relationship, the average surface potential of the channel can be calculated quickly and accurately according to the gate voltage, source voltage, drain voltage, and ferroelectric polarization state. Furthermore, the intermediate node potential can be calculated quickly and accurately based on the first functional relationship and the average surface potential of the channel. In summary, the method for calculating the intermediate node potential of a ferroelectric transistor provided in this application can quickly and accurately calculate the intermediate node potential of the ferroelectric transistor, which is beneficial for quickly calculating the DC conduction current of the ferroelectric transistor channel. Attached Figure Description

[0021] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments of this application will be briefly introduced below. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a flowchart illustrating a method for calculating the intermediate node potential of a ferroelectric transistor according to an embodiment of this application. Figure 2 This is a schematic diagram of the device structure of a ferroelectric transistor provided in one embodiment of this application; Figure 3 This is a flowchart illustrating a method for calculating the intermediate node potential of a ferroelectric transistor according to an embodiment of this application. Figure 4 The quasi-static transfer characteristic curve of FeFET and the memory window characteristic diagram after programming are obtained by simulation calculation using the method of this application and traditional solution method; Figure 5 The figure shows the dynamic simulation results of calculating the channel conduction current using the method of this application and traditional solution methods. Figure 6 The time consumption of each step in calculating the channel conduction current using the method of this application and conventional solution methods is shown. Figure 7 The time consumption for calculating the channel conduction current using the method of this application, the conventional solution scheme, and the logic transistor model is shown for various time steps. Figure 8 This is a schematic diagram of the hardware structure of an electronic device provided in one embodiment of this application. Detailed Implementation

[0023] The features and exemplary embodiments of various aspects of this application will be described in detail below. To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only intended to explain this application and not to limit it. For those skilled in the art, this application can be implemented without some of these specific details. The following description of the embodiments is merely to provide a better understanding of this application by illustrating examples.

[0024] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus that includes said element.

[0025] First, the background technology involved in this application will be introduced.

[0026] With the arrival of the post-Moore's Law era, the total amount of global data is surging year by year, placing higher demands on data storage and real-time processing. Among various non-volatile memories, ferroelectric field-effect transistors (FeFETs) have significant advantages over traditional embedded flash memory in terms of operating voltage, write power consumption, and write speed. Compared to other novel non-volatile memories, FeFETs can store information by changing the threshold state by altering the polarization state of the ferroelectric material in the gate stack. FeFET memory cells consist of only one transistor, resulting in a simpler cell structure, lower write power consumption, non-destructive readout, and CMOS process compatibility. Therefore, FeFETs have great potential for non-volatile, high-speed, high-density, and low-power embedded memory applications and are currently a hot research topic.

[0027] Large-scale FeFET circuit design requires a compact model that can accurately and efficiently describe the dynamic electrical characteristics of FeFETs. Although several compact FeFET models have been proposed and some progress has been made, significant limitations remain. First, traditional model solution methods typically require a binary search iteration of the potential between the ferroelectric layer and the interface layer, resulting in significant computational overhead. Second, the traditional polycrystalline Monte Carlo NLS model introduces high computational complexity when describing the ferroelectric layer. Finally, traditional models struggle to efficiently incorporate a model of defect-trapped charges, which is crucial for the dynamic characteristics of FeFETs. Therefore, further optimization of the solution efficiency and accuracy of the FeFET compact model is urgently needed.

[0028] Therefore, the current FeFET compact model suffers from the problem of not being able to balance computational efficiency and computational accuracy.

[0029] To address the problems in the prior art, this application provides a method for calculating the potential of the intermediate node of a ferroelectric transistor. This method avoids the high computational overhead of binary search for the potentials of the ferroelectric layer and the interface layer. It uses a nonlinear NLS model based on energy domain partitioning to describe the ferroelectric layer and combines it with the SRH theory defect charge model based on spatial domain partitioning. This significantly improves the solution speed and accuracy of the FeFET compact model and achieves efficient calculation of the coupling between ferroelectric spontaneous polarization and defect charge charging and discharging.

[0030] The following section first introduces the method for calculating the intermediate node potential of the ferroelectric transistor provided in the embodiments of this application.

[0031] Figure 1 This is a flowchart illustrating a method for calculating the intermediate node potential of a ferroelectric transistor according to an embodiment of this application. Figure 1 As shown in the embodiments of this application, the method for calculating the intermediate node potential of a ferroelectric transistor includes: Step 101: Based on the charge conservation relationship between the gate oxide layer and the semiconductor portion in the ferroelectric transistor, and after averaging the channel potential, determine the first functional relationship between the intermediate node potential and the average surface potential of the channel. Step 102, combined with the conservation of ferroelectric layer charge, determines the second functional relationship between the channel average surface potential and the gate voltage, source voltage, drain voltage, ferroelectric polarization state and defect occupancy state; Step 103: Based on the second functional relationship, and combined with the first functional relationship for elimination, calculate the average surface potential of the channel according to the gate voltage, source voltage, drain voltage, ferroelectric polarization state and defect occupancy state. Step 104: Calculate the intermediate node potential based on the first functional relationship and the average surface potential of the channel.

[0032] In some embodiments, step 104 is followed by: Step 105: Calculate the source-end surface potential and drain-end surface potential based on the intermediate node potential, source voltage, and drain voltage. Step 106: Calculate the channel DC conduction current based on the intermediate node potential, the source end surface potential, and the drain end surface potential.

[0033] In some embodiments, step 106 is followed by: Step 107: Update the ferroelectric polarization state based on the intermediate node potential and gate voltage; update the source and drain surface potentials based on the intermediate node potential and the updated ferroelectric polarization state.

[0034] In some embodiments, the method for calculating the intermediate node potential of a ferroelectric transistor provided in this application is used to calculate the intermediate node potential of a ferroelectric transistor in a SPICE simulator or scientific computing tools such as Matlab or Python, thereby realizing the calculation of the channel current of the ferroelectric transistor.

[0035] In some embodiments, the initial state of the ferroelectric transistor is first set, including the ferroelectric polarization state. Defect occupancy rate Set time step At the current time point It is known that the voltage bias of a ferroelectric transistor (FeFET) is equal to the source voltage. Drain voltage Body terminal voltage and gate voltage According to the polarization state of ferroelectric transistors and defect occupancy rate The defect charge in the interface layer of the ferroelectric transistor was calculated. .

[0036] In some embodiments, the charge conservation relationship between the gate oxide layer and the semiconductor portion of the ferroelectric transistor includes the relationship between the charge quantity and potential at various points in the equations for the ferroelectric portion and the transistor's MOS portion, based on the current ferroelectric polarization state. and the amount of defect charge in the interface layer The relationship between the charge and potential at various points in the equations for the ferroelectric part and the transistor MOS part is obtained as follows: (1), (2), (3), (4), in, To inject defect charges into the interface layer. For the charge between the ferroelectric layer and the interface layer, in some embodiments, for FeFETs of the MFMIS type with an intermediate layer, The charge is for the intermediate layer metal; for MFIS type FeFETs, The interfacial charge of the ferroelectric layer / interface layer. The capacitance per unit area of ​​the ferroelectric layer. This represents the capacitance per unit area of ​​the interface layer. The vacuum permittivity, The relative permittivity of the ferroelectric layer material is . The thickness of the ferroelectric layer material, The relative permittivity of the interface layer material is denoted as . The thickness of the interface layer material.

[0037] in, Let be the surface potential of the channel, which is the quantity to be solved. This represents the functional relationship between channel charge and channel surface potential, which is related to the channel material. This represents the channel potential.

[0038] In some embodiments, for silicon (Si) materials: (5), in, For symbolic functions, To build internal power, Substrate doping with Si material related, Thermoelectric potential, is the relative permittivity of silicon.

[0039] In some embodiments, for indium gallium zinc oxide (IGZO): (6), in, For the channel potential, (7), in, , , These represent the density of conduction band electrons, band tail electrons, and interface defect states, respectively.

[0040] In some embodiments, in order to accurately determine the first functional relationship, step 102, refinement includes: Step 201: Based on the charge conservation relationship between the gate oxide layer and the semiconductor part in the ferroelectric transistor, determine the third function relationship between the intermediate node potential and the channel surface potential. Step 202: Determine the channel average potential based on the source voltage and the effective drain voltage; wherein the effective drain voltage is determined based on the source voltage, drain voltage, and saturated drain voltage, and the saturated drain voltage is determined based on the gate voltage, source voltage, transistor threshold voltage, and transistor body effect coefficient. Step 203, based on ferroelectric materials and channel average potential Determine the average surface potential of the channel The fourth function relationship with channel charge ; Step 204: Determine the first functional relationship based on the third and fourth functional relationships.

[0041] In some embodiments, the channel potential is averaged. From source voltage V S and drain voltage V D Joint decision: (8), (9), (10) Among them, V T is the threshold voltage of the transistor FET section, and m is the body effect coefficient of the transistor FET section. Both can be determined given the channel material parameters.

[0042] Furthermore, for silicon (Si) materials, the potential of the channel portion is averaged to obtain: (11), (12) For silicon (Si) materials, the third functional relationship is given by formula (11), and the fourth functional relationship is given by formula (12). The potential of the channel portion is averaged, and the potential of the intermediate node is determined according to formulas (11) and (12). With channel average surface potential The first functional relationship.

[0043] For indium gallium zinc oxide (IGZO), the channel potential is averaged to obtain: (13) (14) For indium gallium zinc oxide (IGZO), the third functional relationship is given by formula (13), and the fourth functional relationship is given by formula (14). The channel potential is averaged, and the intermediate node potential is determined according to formulas (13) and (14). With channel average surface potential The first functional relationship.

[0044] The first functional relationship is: (15) In some embodiments, in order to accurately determine the second functional relationship, step 102 is further refined to include: Step 401: Based on the first functional relationship, the first expression for the metal gate charge, the second expression for the metal gate charge, and the third expression for the transistor equivalent charge, construct the second functional relationship. During the construction of the second functional relationship, based on the first functional relationship, use the channel average surface potential to express the intermediate node potential, so that the constructed second functional relationship does not contain an intermediate node potential. The first expression represents the charge conservation relationship between the metal gate charge, the ferroelectric polarization state, the gate voltage, and the intermediate node potential; the second expression represents the charge conservation relationship between the metal gate charge, the transistor equivalent charge, and the intermediate metal layer charge; and the third expression represents the charge conservation relationship between the transistor equivalent charge, the intermediate node potential, the flat-band voltage, and the channel average surface potential.

[0045] Specifically, the first expression is formula (1): , The second expression is formula (3). , The third expression is formula (2). , in, This refers to the charge on the metal gate. It is in the ferropolar polarization state. Gate voltage, The potential at the intermediate node. The capacitance per unit area of ​​the ferroelectric layer. This is the equivalent charge of the transistor. The charge is that of the intermediate metal layer. It is a flat band voltage. The average surface potential of the channel is... This refers to the capacitance per unit area of ​​the interface layer. Furthermore, based on the first functional relationship, the first expression for the metal gate charge, the second expression for the metal gate charge, and the third expression for the transistor equivalent charge, the second functional relationship is constructed as follows: Substituting the first functional relationship into the first expression, we obtain the fourth expression: (16) Substituting the first functional relationship into the third expression, we obtain the fifth expression: (17) Substituting the fourth and fifth expressions into the second expression, we get: (18) Transforming formula (18) yields the second functional relationship: (19) Step 103, based on the second functional relationship, according to the gate voltage Source voltage Drain voltage and ferropolar polarization state Calculate the average surface potential of the channel .

[0046] After obtaining the second functional relation, the second functional relation is about The single-variable transcendental equation can be solved quickly using Newton's iteration method, yielding the following results. .

[0047] Step 104, based on the first functional relationship and the average surface potential of the channel. Calculate the potential at intermediate nodes .

[0048] In obtaining Then, the intermediate node potential can be further solved according to the first functional relationship, such as formula (11) or formula (13). .

[0049] Step 105, based on the intermediate node potential Source voltage and drain voltage Calculate the source-end surface potential and the surface potential of the drain end .

[0050] Solving for the potential at the intermediate node Then, V mid V S V D Considering the three-terminal bias of the transistor FET section, we obtain two equations similar to formula (4): (20) (twenty one), Will Substitute into formulas (20) and (21) to solve for the corresponding source-drain surface potentials. .

[0051] Step 106, based on the intermediate node potential Source end surface potential and the surface potential of the drain end Calculate the DC conduction current of the channel .

[0052] In some embodiments, a charge-thin layer approximation model is used to calculate the channel DC conduction current for Si materials. The formula is as follows: (twenty two) in, For electron mobility, W The width of the channel. L The length of the channel. The Debye length is the channel semiconductor material.

[0053] In some embodiments, for IGZO materials, the approximate treatment is as follows: (twenty three).

[0054] The method for calculating the intermediate node potential of a ferroelectric transistor provided in this application embodiment calculates the channel potential by... In the case of averaging, and based on the charge conservation relationship between the gate oxide layer and the semiconductor portion in the ferroelectric transistor, a first functional relationship between the intermediate node potential and the channel average surface potential is determined. Then, based on this first functional relationship, the intermediate node potential is eliminated, and a second functional relationship between the channel average surface potential and the gate voltage, source voltage, drain voltage, and ferroelectric polarization state is determined. Based on this second functional relationship, the channel average surface potential can be calculated quickly and accurately using the gate voltage, source voltage, drain voltage, and ferroelectric polarization state. Similarly, the intermediate node potential can be calculated quickly and accurately using the first functional relationship and the channel average surface potential. This allows for the rapid and accurate calculation of the intermediate node potential of the ferroelectric transistor. Furthermore, while maintaining the accuracy of calculating the channel DC conduction current of the ferroelectric transistor, the speed of calculating the channel DC conduction current is improved.

[0055] In some embodiments, gate voltage Source voltage and drain voltage As time-series data, ferroelectric polarization and defect occupancy states are also time-series data; therefore, the channel DC conduction current... This is also time-series data, used for efficient and accurate calculation of the channel DC conduction current. Step 106 is followed by step 107 to complete the device state update. Step 107 is further detailed as follows: Step 601: Calculate the ferroelectric layer field size at time i based on the gate voltage and the intermediate node potential at time i; time i can be any time point in the timing sequence. Step 602: Calculate the ferroelectric polarization state at time i+1 based on the magnitude of the ferroelectric layer field at time i. Step 603: Based on the ferroelectric polarization state at time i+1, and assuming that the defects with trap energy levels are spatially uniformly distributed in the interface, calculate the defect charge at time i+1. Step 604, based on the gate voltage at time point i+1 Source voltage Drain voltage Given the defect charge, calculate the channel DC conduction current at time i+1.

[0056] In some embodiments, at time i+1, the ferroelectric polarization state is determined by a series of... , Describing by size, and The sum is 1. A coefficient describing the distribution of activation energy in the ferroelectric layer, with values ​​ranging from 0 to... of Divide equally. Based on accuracy requirements, and The value can be adjusted.

[0057] In some embodiments, step 601 is further refined to include: Step 901: Based on the magnitude of the ferroelectric layer field at time point i, and assuming that defects with trap energy levels are spatially uniformly distributed in the interface, calculate the relative energy difference between the channel conduction band and the defect energy level. Step 902: Calculate the charge / discharge barrier based on the relative energy difference; Step 903: Calculate the tunneling probability of defects with trap energy levels when they are spatially uniformly distributed in the interface, based on the band shift and charge / discharge barrier between the interface layer and the channel. Step 904: Calculate the transition rate between occupied and unoccupied states of a defect with a trap energy level based on the tunneling probability; Step 905: Based on the probability that a defect with a trap energy level is in an occupied state at time i, the transition rate, and the unit time length, calculate the probability that a defect with a trap energy level is in an occupied state at time i+1. Step 906: Calculate the defect charge at time i+1 based on the probability that the defect with the trap energy level is in an occupied state at time i+1.

[0058] In some embodiments, considering the presence of trap energy levels The defects are uniformly distributed in the space of the interface layer, and the interface layer is geometrically along the channel direction. Divide into equal parts, for one part For defects at specific locations, calculate the relative energies of the channel conduction band and defect levels based on the current electric field magnitude at the interface layer. Thus, the charging and discharging barriers are obtained: (24), among which, The number of spatial discretizations or mesh divisions for the interface layer. A barrier to trap channel electrons for interface layer defects. This acts as a barrier for the release of electrons from interface layer defects into the channel.

[0059] Simultaneously, based on the interface layer and channel band shift, combined with and defect location The probability of tunneling is approximated based on WKB. .

[0060] Thus, the defect in the occupied state is obtained. non-occupied state Conversion rate between: (25), of which, N c For the effective density of states in the conduction band, σ n For the electron trapping cross-sectional area, v thermal The average thermal velocity of the charge carriers. k 12 For defects from non-occupied state p 1 To occupy state p 2 Conversion rate, k 21 For defects from occupied state p 1 to non-occupied state p 2 Conversion rate, q The amount of charge per unit charge. k Boltzmann's constant, T Absolute temperature is expressed in Kelvin.

[0061] Based on the i-th time point Based on the conversion rate and time step, the occupancy rate at time point i+1 is calculated. (26), where Δ t For time step.

[0062] Based on the occupancy rate at time point i+1, the defect electron charge at time point i+1 is calculated as follows: (27), among which, NT This represents the spatial density of defects in the interface layer.

[0063] The method for calculating the intermediate node potential of a ferroelectric transistor provided in this application takes into account the presence of trap energy levels. The defects are uniformly distributed in the space of the interface layer, which allows for the rapid calculation of the charge and discharge barrier, and thus the rapid calculation of the defect electron charge at time point i+1.

[0064] The method for calculating the intermediate node potential of a ferroelectric transistor provided in this application, by updating the defect charge at time point i+1, can calculate the potential based on the gate voltage at time point i+1. Source voltage Drain voltage By calculating the channel DC conduction current at time i+1 and the defect charge, it is possible to calculate the DC conduction current of the ferroelectric transistor at each time point, and thus realize the calculation of large-scale FeFET circuits.

[0065] In some embodiments, step 602 is further refined to include: Step 701: Calculate the polarization reversal time constant of the ferroelectric layer activation energy distribution coefficient based on the ferroelectric layer field magnitude at time point i. ; Step 702, based on the polarization reversal time constant The ferropolarization state at time i+1 is calculated using a preset time function; the preset time function decays exponentially from 1 to 0 as time increases.

[0066] In some embodiments, a function is used that decays exponentially from 1 to 0 over time. The time dependence of the distribution coefficient of the activation energy of the ferroelectric layer is described, where, (28).

[0067] in, The attenuation coefficient is... It is a natural exponential function. For a point in time, The polarization reversal time constant. This is a preset constant.

[0068] According to the function Calculate the activation energy of the ferroelectric layer. Decay from 1 to the i-th time point Equivalent time Therefore, the state at time i+1 is the state after decaying from 1 to the equivalent time plus the time step, and the update value is... .

[0069] Therefore, the polarization at time point i+1 is equal to , in, ,in, To describe the second type of Beta distribution of activation energy distribution, This represents the saturated remanent polarization of ferroelectric materials.

[0070] In some embodiments, starting from an initial time point, the ferroelectric state and defect occupancy rate are calculated using the method described above at each subsequent time point, and then the gate voltage at each time point is used as a basis for calculation. Source voltage and drain voltage Calculate the conduction current at each time point This allows us to fully describe the dynamic behavior of FeFET under arbitrary waveforms.

[0071] The method for calculating the intermediate node potential of a ferroelectric transistor provided in this application employs a function that decays exponentially from 1 to 0 over time. The time dependence of the activation energy distribution coefficient of the ferroelectric layer is described, which enables the rapid and accurate calculation of the polarization of the ferroelectric transistor at time i+1.

[0072] Figure 2 This is a schematic diagram of the device structure of a ferroelectric transistor provided in one embodiment of this application. Figure 2 The ferroelectric transistor device structure provided in one embodiment of this application includes: a silicon substrate Si and a silicon oxide isolation layer SiO2, a gate electrode G, a ferroelectric layer FE, an intermediate metal layer MG, a gate oxide layer OX, a channel layer, a source electrode S, and a drain electrode D. The gate electrode G, the intermediate metal layer MG, the source electrode S, and the drain electrode D can be made of TiN material; the ferroelectric layer FE can be made of zirconium-doped hafnium oxide; the gate oxide layer OX can be made of hafnium oxide; and the channel layer can be made of amorphous IGZO.

[0073] Figure 3 This is a flowchart illustrating a method for calculating the intermediate node potential of a ferroelectric transistor according to an embodiment of this application. Figure 3 As shown, it includes the following steps: S311, Initialization: Given the polarization state and defect occupancy state.

[0074] S312, given V G V S V D V B Waveform.

[0075] S313, determine t i The time-point bias state, ferroelectric planning state, and interface layer defect charge.

[0076] S314, The objective is defined as: finding the V that balances the gate charge. mid .

[0077] S315, according to V mid Calculate the channel conduction current I ds .

[0078] S316, according to V mid and time step t step Update the polarization state and update the defect-occupied state.

[0079] S317, Determine if time t is greater than the total time t. total ? S318, if so, then the process ends.

[0080] S319, otherwise according to time step t step Update time t i And repeat steps S313 to S317.

[0081] Step S313 includes steps S3131 to S3133.

[0082] S3131, Obtain partial charge balance of MOS: (V mid -V FB -φ s,avg )*C ox -Q s (φ s,avg )-Q T =0, and the partial charge balance of FE: P FE +(V G -V mid )*C FE -(V mid -V fb -φ s,avg )*C ox -Q f =0 S3132, based on the partial charge balance of MOS and the partial charge balance of FE, eliminate Vmid to obtain information about φ. s,avg A single-variable transcendental equation.

[0083] S3133, using Newton's iteration method to solve for φ in S3132. s,avg The single-variable transcendental equation, subsequently based on φ s,avg Calculate V mid .

[0084] In some embodiments, a method for calculating the intermediate node potential of a ferroelectric transistor provided in one embodiment of this application includes: 1) Set the initial state of the device, including its ferroelectric polarization state. Defect occupancy rate .

[0085] 2) Set the time step At the current time point The corresponding charge is calculated from the polarization state and the defect occupancy rate.

[0086] 3) At the current bias voltage V G V S V D V B Based on the charge balance equation and the properties of the MOS structure, a series of equations are derived. Using the method of this invention, the intermediate node potential is eliminated and transformed into a single-variable equation for the surface potential. Thus, the surface potential can be calculated in only one iteration, and the electric field of each part of the ferroelectric gate stack can be obtained.

[0087] 4) Calculate the DC conduction current in the channel based on the intermediate node potential and the channel surface potential. .

[0088] 5) Update the polarization state of the ferroelectric layer at the next time step based on the electric field magnitude of the ferroelectric layer and the analytical NLS model.

[0089] 6) Calculate the potential barrier for defect charging and discharging based on the interface layer electric field and defect energy levels. The probability of tunneling is calculated based on the spatial location and energy band of the defect. The transition rate between the occupied and unoccupied states of the defect is further calculated, thereby calculating the defect occupancy rate for the next time step. .

[0090] 7) As time progresses, calculate and record the device state and current at each moment. .

[0091] Figure 4 The quasi-static transfer characteristic curve of the FeFET and the memory window characteristic diagram after programming are obtained by simulation calculation using the method of this application and traditional solution methods when the channel conduction current is reached. Figure 4 As shown, sim represents the channel conduction current calculated using the method described in this application. exp is the channel current obtained from the actual experiment. sim and The fact that the exp values ​​are essentially the same further proves the accuracy of the calculation method for the intermediate node potential of the ferroelectric transistor provided in this application.

[0092] Figure 5The figures show the dynamic simulation results of the channel conduction current calculated using the method of this application and traditional solution methods. Figure 5 As shown, when the channel material and input voltage are the same, the channel conduction current is calculated using the method of this application and the conventional solution method. Under the conditions of a 200-microsecond triangular wave and a time of 1 microsecond, the calculation results of the method of this application and the conventional solution method are the same and the calculation time is shorter, which further proves the accuracy and calculation efficiency of the method for calculating the intermediate node potential of ferroelectric transistors provided in this application.

[0093] Figure 6 The time consumption of each step in calculating the channel conduction current using the method of this application and conventional methods is shown. For example... Figure 6 As shown, the time optimization of the method in this application mainly lies in the search process for intermediate nodes.

[0094] Figure 7 The time consumption for calculating the channel conduction current using the method of this application, conventional solution schemes, and logic transistor models is shown at various time steps. Figure 7 In this paper, the traditional solution scheme is represented by the traditional framework FeFET compact model, while the method of this application is represented by the FeFET compact model provided in this application. The FeFET compact model provided in this application optimizes the computational overhead of the traditional model when processing coupled physical images, and realizes an accurate, efficient, and SPICE-compatible compact model, providing strong support for the circuit simulation of related devices. Figure 7 The time consumption of the FeFET compact model of the present invention under various time steps is given, and compared with the time consumption of traditional solution schemes and logic transistor models: thanks to the optimization of the solution scheme, the new framework achieves more than ten times the energy efficiency improvement compared with the traditional framework; and because the complexity of defect charge handling is low, the time cost of the model of the present invention is only 2.5 times that of the logic transistor model.

[0095] like Figure 7As shown, at time steps of 1μs, 110ns, 20ns, 1ns, and 100ps, the time consumption for calculating the channel conduction current using the conventional solution method is 1.05s, 9.234s, 90.5s, 1099s, and 14365s, respectively. The time consumption for calculating the intermediate node potential of the ferroelectric transistor provided in this application is 0.090s, 0.734s, 3.813s, 48.75s, and 1078s, respectively. The time consumption for calculating the channel conduction current using the logic transistor model is 0.0446s, 0.2922s, 1.6940s, 16.901s, and 498.1s, respectively. It can be seen that the method of this application has a more than tenfold improvement in energy efficiency compared to the conventional solution method. Furthermore, due to the lower complexity of defect charge handling, the time cost of the model of this invention is only 2.5 times that of the logic transistor model.

[0096] In some embodiments, the method for calculating the intermediate node potential of a ferroelectric transistor includes: Calculate the average surface potential of the channel based on the source voltage and drain voltage; Based on the charge conservation relationship between the gate oxide layer and the semiconductor portion in a ferroelectric transistor, and after averaging the channel potential, the first functional relationship between the intermediate node potential and the average surface potential of the channel is determined. By combining the conservation of ferroelectric layer charge, a second functional relationship between the channel average surface potential and the gate voltage, source voltage, drain voltage, ferroelectric polarization state, and defect charge is determined. Based on the second functional relationship, and combined with the first functional relationship for elimination, the average surface potential of the channel is calculated according to the gate voltage, source voltage, drain voltage, ferroelectric polarization state and defect occupancy state. The intermediate node potential is calculated based on the first functional relationship and the average surface potential of the channel. Calculate the source-end surface potential and the drain-end surface potential based on the intermediate node potential, the source voltage, and the drain voltage; The channel DC conduction current is calculated based on the intermediate node potential, the source end surface potential, and the drain end surface potential. The ferroelectric polarization state is updated based on the intermediate node potential and gate voltage; the source and drain surface potentials are updated based on the intermediate node potential and the updated ferroelectric polarization state.

[0097] One embodiment of this application provides a device for calculating the intermediate node potential of a ferroelectric transistor, comprising: The first determining module is used to determine the channel potential based on the charge conservation relationship between the gate oxide layer and the semiconductor portion in the ferroelectric transistor. Determine the potential at intermediate nodes after averaging. With channel average surface potential The first functional relationship; The second determining module is used to determine the average surface potential of the channel based on the first functional relationship. With gate voltage Source voltage Drain voltage and ferropolar polarization state The second functional relationship; The first calculation module is used to calculate the gate voltage based on the second functional relationship. Source voltage Drain voltage and ferropolar polarization state Calculate the average surface potential of the channel ; The second calculation module is used to calculate based on the first functional relationship and the average surface potential of the channel. Calculate the potential at intermediate nodes .

[0098] In one alternative embodiment, the device for calculating the intermediate node potential of the ferroelectric transistor further includes: The third calculation module is used to calculate the potential of intermediate nodes. Source voltage and drain voltage Calculate the source-end surface potential and the surface potential of the drain end ; The fourth calculation module is used to calculate the potential of intermediate nodes. Source end surface potential and the surface potential of the drain end Calculate the DC conduction current of the channel .

[0099] In one optional implementation, the first determining module is specifically used to: determine the third functional relationship between the intermediate node potential and the channel surface potential based on the charge conservation relationship between the gate oxide layer and the semiconductor portion in the ferroelectric transistor. The average channel potential is determined based on the source voltage and the effective drain voltage; wherein the effective drain voltage is determined based on the source voltage, drain voltage, and saturated drain voltage, and the saturated drain voltage is determined based on the gate voltage, source voltage, transistor threshold voltage, and transistor body effect coefficient. The fourth functional relationship between the average surface potential of the channel and the channel charge is determined based on ferroelectric materials and the average channel potential. The first functional relationship is determined based on the third functional relationship and the fourth functional relationship.

[0100] In one alternative implementation, the channel average potential Represented as: ,in, Source voltage, For effective drain voltage, ;in, Drain voltage This is the saturation drain voltage. ;in, Gate voltage, is the transistor threshold voltage, and m is the transistor bulk effect coefficient; The first functional relationship is expressed as: ,in, The potential at the intermediate node. It is a flat band voltage. The average surface potential of the channel is... For the channel potential, To determine the relationship between channel charge and channel surface potential based on ferroelectric materials. This refers to the capacitance per unit area of ​​the interface layer. This refers to the amount of defect charge injected into the interface layer.

[0101] In an optional implementation, the second determining module is specifically used to: construct the second functional relationship based on the first functional relationship, the first expression of the metal gate charge, the second expression of the metal gate charge, and the third expression of the transistor equivalent charge; and in the process of constructing the second functional relationship, based on the first functional relationship, use the channel average surface potential to express the intermediate node potential so that there is no intermediate node potential in the constructed second functional relationship. Wherein, the first expression is the charge conservation relationship between the metal gate charge and the ferroelectric polarization state, gate voltage, and intermediate node potential; the second expression is the charge conservation relationship between the metal gate charge and the transistor equivalent charge and the intermediate metal layer charge; and the third expression is the charge conservation relationship between the transistor equivalent charge and the intermediate node potential, flat band voltage, and channel average surface potential.

[0102] In one alternative implementation, the first expression is: , The second expression is , The third expression is , in, This refers to the charge on the metal gate. It is in the ferropolar polarization state. Gate voltage, The potential at the intermediate node. The capacitance per unit area of ​​the ferroelectric layer. This is the equivalent charge of the transistor. The charge is that of the intermediate metal layer. It is a flat band voltage. The average surface potential of the channel is... This refers to the capacitance per unit area of ​​the interface layer. Based on the first functional relationship, the metal gate charge First expression, metal gate charge The second expression and the transistor equivalent charge The third expression constructs the second functional relationship, including: Substituting the first functional relationship into the first expression, we obtain the fourth expression; Substituting the first functional relationship into the third expression, we obtain the fifth expression; Substitute the fourth and fifth expressions into the second expression to obtain the second functional relationship; The second functional relationship is: ,in, This refers to the amount of defect charge injected into the interface layer.

[0103] In one optional embodiment, the gate voltage, the source voltage, and the drain voltage are timing data, and the device for calculating the intermediate node potential of the ferroelectric transistor further includes a fifth calculation module, which is used for: The magnitude of the ferroelectric layer field at time i is calculated based on the gate voltage and the intermediate node potential at time i; where time i is any time point in the timing sequence. Calculate the ferroelectric polarization state at time i+1 based on the magnitude of the ferroelectric layer field at time i. Based on the ferroelectric polarization state at time i+1, and assuming that the defects with trap energy levels are spatially uniformly distributed in the interface, calculate the defect charge at time i+1. Calculate the channel DC conduction current at time i+1 based on the gate voltage, source voltage, drain voltage, and defect charge at time i+1.

[0104] In an optional implementation, the fifth calculation module is further configured to: The polarization reversal time constant is calculated based on the ferroelectric field magnitude at time point i, which is the distribution coefficient of the ferroelectric activation energy. ; Based on polarization reversal time constant The ferropolarization state at time i+1 is calculated using a preset time function; the preset time function decays exponentially from 1 to 0 as time increases.

[0105] In one optional implementation, the preset time function is expressed as: ,in, The attenuation coefficient is... It is a natural exponential function. For a point in time, The polarization reversal time constant. This is a preset constant.

[0106] In an optional implementation, the fifth calculation module is further configured to: Based on the magnitude of the ferroelectric layer field at time point i, and assuming that defects with trap energy levels are spatially uniformly distributed in the interface, the relative energy difference between the channel conduction band and the defect energy level is calculated. Calculate the charging and discharging barrier based on the relative energy difference; Based on the band shift and charge / discharge barrier between the interface layer and the channel, the tunneling probability is calculated when the defect with trap energy level is spatially uniformly distributed in the interface. The transition rate between occupied and unoccupied states of a defect with a trap energy level is calculated based on the tunneling probability. Based on the probability, transition rate, and unit time length of a defect with a trap energy level being in an occupied state at time i, calculate the probability of a defect with a trap energy level being in an occupied state at time i+1. Calculate the defect charge at time i+1 based on the probability that a defect with a trap energy level is in an occupied state at time i+1.

[0107] Figure 8 This is a schematic diagram of the hardware structure of an electronic device provided in one embodiment of this application. For example... Figure 8 As shown, the electronic device provided in this application embodiment may include a processor 81 and a memory 82 storing computer program instructions.

[0108] Specifically, the processor 81 may include a central processing unit (CPU), an application-specific integrated circuit (ASIC), or one or more integrated circuits that can be configured to implement the embodiments of this application.

[0109] Memory 82 may include mass storage for data or instructions. For example, and not limitingly, memory 82 may include a hard disk drive (HDD), floppy disk drive, flash memory, optical disk, magneto-optical disk, magnetic tape, or Universal Serial Bus (USB) drive, or a combination of two or more of these. Where appropriate, memory 82 may include removable or non-removable (or fixed) media. Where appropriate, memory 82 may be internal or external to the integrated gateway disaster recovery device. In a particular embodiment, memory 82 is non-volatile solid-state memory.

[0110] Memory may include read-only memory (ROM), random access memory (RAM), disk storage media devices, optical storage media devices, flash memory devices, and electrical, optical, or other physical / tangible memory storage devices. Therefore, typically, memory includes one or more tangible (non-transitory) computer-readable storage media (e.g., memory devices) encoded with software including computer-executable instructions, and when the software is executed (e.g., by one or more processors), it is operable to perform the operations described with reference to the method according to one aspect of this application.

[0111] The processor 81 reads and executes computer program instructions stored in the memory 82 to implement any of the methods for calculating the intermediate node potential of the ferroelectric transistor in the above embodiments.

[0112] In one example, the electronic device may also include a communication interface 83 and a bus 84. Wherein, such as Figure 8 As shown, the processor 81, memory 82, and communication interface 83 are connected through bus 84 and complete communication with each other.

[0113] Communication interface 83 is mainly used to realize communication between various modules, devices, units and / or equipment in the embodiments of this application.

[0114] Bus 84 includes hardware, software, or both, that couples components of an online data traffic metering device together. For example, and not limitingly, the bus may include an Accelerated Graphics Port (AGP) or other graphics bus, an Enhanced Industry Standard Architecture (EISA) bus, a Front Side Bus (FSB), HyperTransport (HT) interconnect, an Industry Standard Architecture (ISA) bus, an Infinite Bandwidth Interconnect, a Low Pin Count (LPC) bus, a memory bus, a Microchannel Architecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, a PCI-Express (PCI-X) bus, a Serial Advanced Technology Attachment (SATA) bus, a Video Electronics Standards Association Local (VLB) bus, or other suitable buses, or combinations of two or more of these. Where appropriate, bus 84 may include one or more buses. Although specific buses are described and illustrated in embodiments of this application, any suitable bus or interconnect is contemplated herein.

[0115] Furthermore, in conjunction with the calculation method for the intermediate node potential of the ferroelectric transistor in the above embodiments, this application embodiment can provide a computer-readable storage medium for implementation. This computer-readable storage medium stores computer program instructions; when executed by a processor, these computer program instructions implement any of the calculation methods for the intermediate node potential of the ferroelectric transistor in the above embodiments.

[0116] This application also provides a computer program product, including a computer program that, when executed, implements any of the methods for calculating the intermediate node potential of a ferroelectric transistor in the above embodiments.

[0117] It should be clarified that this application is not limited to the specific configurations and processes described above and shown in the figures. For the sake of brevity, detailed descriptions of known methods are omitted here. In the above embodiments, several specific steps are described and shown as examples. However, the method process of this application is not limited to the specific steps described and shown. Those skilled in the art can make various changes, modifications, and additions, or change the order of steps, after understanding the spirit of this application.

[0118] The functional blocks shown in the above-described structural diagram can be implemented as hardware, software, firmware, or a combination thereof. When implemented in hardware, they can be, for example, electronic circuits, application-specific integrated circuits (ASICs), appropriate firmware, plug-ins, function cards, etc. When implemented in software, the elements of this application are programs or code segments used to perform the required tasks. Programs or code segments can be stored on a machine-readable medium or transmitted over a transmission medium or communication link via data signals carried on a carrier wave. "Machine-readable medium" can include any medium capable of storing or transmitting information. Examples of machine-readable media include electronic circuits, semiconductor memory devices, ROM, flash memory, erasable ROM (EROM), floppy disks, CD-ROMs, optical disks, hard disks, fiber optic media, radio frequency (RF) links, etc. Code segments can be downloaded via computer networks such as the Internet, intranets, etc.

[0119] It should also be noted that the exemplary embodiments mentioned in this application describe methods or systems based on a series of steps or apparatus. However, this application is not limited to the order of the above steps; that is, the steps can be performed in the order mentioned in the embodiments, or in a different order, or several steps can be performed simultaneously.

[0120] The aspects of this disclosure have been described above with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It should be understood that each block in the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that these instructions, executable via the processor of the computer or other programmable data processing apparatus, enable the implementation of the functions / actions specified in one or more blocks of the flowchart illustrations and / or block diagrams. Such a processor can be, but is not limited to, a general-purpose processor, a special-purpose processor, a special application processor, or a field-programmable logic circuit. It is also understood that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can also be implemented by special-purpose hardware performing the specified functions or actions, or can be implemented by a combination of special-purpose hardware and computer instructions.

[0121] The above description is merely a specific implementation of this application. Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, modules, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here. It should be understood that the protection scope of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in this application, and these modifications or substitutions should all be covered within the protection scope of this application.

Claims

1. A method for calculating the potential at the intermediate node of a ferroelectric transistor, characterized in that, include: Based on the charge conservation relationship between the gate oxide layer and the semiconductor portion in a ferroelectric transistor, and after averaging the channel potential, the first functional relationship between the intermediate node potential and the average surface potential of the channel is determined. By combining the charge conservation relationship of the ferroelectric layer, a second functional relationship between the channel average surface potential and the gate voltage, source voltage, drain voltage, ferroelectric polarization state and defect charge is determined; Based on the second functional relationship, and combined with the first functional relationship for elimination, the average surface potential of the channel is calculated according to the gate voltage, source voltage, drain voltage, ferroelectric polarization state and defect occupancy state. The intermediate node potential is calculated based on the first functional relationship and the average surface potential of the channel.

2. The method according to claim 1, characterized in that, After calculating the intermediate node potential based on the first functional relationship and the channel average surface potential, the method further includes: Calculate the source-end surface potential and the drain-end surface potential based on the intermediate node potential, the source voltage, and the drain voltage; The channel DC conduction current is calculated based on the intermediate node potential, the source end surface potential, and the drain end surface potential.

3. The method according to claim 1 or 2, characterized in that, The step of determining the first functional relationship between the intermediate node potential and the average surface potential of the channel, based on the charge conservation relationship between the gate oxide layer and the semiconductor portion in the ferroelectric transistor and after averaging the channel potential, includes: Based on the charge conservation relationship between the gate oxide layer and the semiconductor part in the ferroelectric transistor, the third function relationship between the intermediate node potential and the channel surface potential is determined. The average channel potential is determined based on the source voltage and the effective drain voltage; wherein the effective drain voltage is determined based on the source voltage, drain voltage, and saturated drain voltage, and the saturated drain voltage is determined based on the gate voltage, source voltage, transistor threshold voltage, and transistor body effect coefficient. The fourth functional relationship between the average surface potential of the channel and the channel charge is determined based on ferroelectric materials and the average channel potential. The first functional relationship is determined based on the third functional relationship and the fourth functional relationship.

4. The method according to claim 3, characterized in that, The average potential of the channel is expressed as: ,in, The channel average potential, Source voltage, For effective drain voltage, ;in, Drain voltage This is the saturation drain voltage. ;in, Gate voltage, is the transistor threshold voltage, and m is the transistor bulk effect coefficient; The first functional relationship is expressed as: ,in, The potential at the intermediate node. It is a flat band voltage. The average surface potential of the channel is given by [the value of the channel]. For the channel potential, To determine the relationship between channel charge and channel surface potential based on ferroelectric materials, This refers to the capacitance per unit area of ​​the interface layer. This refers to the amount of defect charge injected into the interface layer.

5. The method according to claim 1 or 2, characterized in that, The step of determining the second functional relationship between the channel average surface potential and the gate voltage, source voltage, drain voltage, and ferroelectric polarization state based on the first functional relationship includes: Based on the first functional relationship, the first expression for the metal gate charge, the second expression for the metal gate charge, and the third expression for the transistor equivalent charge, the second functional relationship is constructed. In the process of constructing the second functional relationship, based on the first functional relationship, the channel average surface potential is used to express the intermediate node potential so that there is no intermediate node potential in the constructed second functional relationship. Wherein, the first expression is the charge conservation relationship between the metal gate charge and the ferroelectric polarization state, gate voltage, and intermediate node potential; the second expression is the charge conservation relationship between the metal gate charge and the transistor equivalent charge and the intermediate metal layer charge; and the third expression is the charge conservation relationship between the transistor equivalent charge and the intermediate node potential, flat band voltage, and channel average surface potential.

6. The method according to claim 5, characterized in that, The first expression is , The second expression is , The third expression is , Among them, the This refers to the charge on the metal gate. It is in the ferropolar polarization state. Gate voltage, The potential at the intermediate node. The capacitance per unit area of ​​the ferroelectric layer. This is the equivalent charge of the transistor. The charge is that of the intermediate metal layer. It is a flat band voltage. The average surface potential of the channel is given by [the value of the channel]. This refers to the capacitance per unit area of ​​the interface layer. The step of constructing the second functional relationship based on the first functional relationship, the first expression for the metal gate charge, the second expression for the metal gate charge, and the third expression for the transistor equivalent charge includes: Substitute the first functional relationship into the first expression to obtain the fourth expression; Substituting the first functional relationship into the third expression, we obtain the fifth expression; Substitute the fourth and fifth expressions into the second expression to obtain the second functional relationship; The second functional relationship is: ,in, This refers to the amount of defect charge injected into the interface layer.

7. The method according to claim 2, characterized in that, The gate voltage, the source voltage, and the drain voltage are timing data. After calculating the channel DC conduction current based on the intermediate node potential, the source end surface potential, and the drain end surface potential, the method further includes: The magnitude of the ferroelectric layer field at time i is calculated based on the gate voltage and the intermediate node potential at time i; where time i is any time point in the timing sequence. Calculate the ferroelectric polarization state at time i+1 based on the magnitude of the ferroelectric layer field at time i. Based on the ferroelectric polarization state at time i+1, and assuming that the defects with trap energy levels are spatially uniformly distributed in the interface, calculate the defect charge at time i+1. Calculate the channel DC conduction current at time i+1 based on the gate voltage, source voltage, drain voltage, and defect charge at time i+1.

8. The method according to claim 7, characterized in that, The calculation of the ferroelectric polarization state at time i+1 based on the magnitude of the ferroelectric layer field at time i includes: The polarization reversal time constant is calculated based on the ferroelectric field magnitude at time point i, which is the distribution coefficient of the ferroelectric activation energy. ; Based on the polarization reversal time constant The ferropolarization state at time point i+1 is calculated using a preset time function; the preset time function decays exponentially from 1 to 0 as time increases.

9. The method according to claim 8, characterized in that, The preset time function is expressed as follows: ,in, The attenuation coefficient is... It is a natural exponential function. For a point in time, The polarization reversal time constant. This is a preset constant.

10. The method according to any one of claims 7 to 9, characterized in that, The step of calculating the defect charge at time i+1 based on the ferroelectric polarization state at time i+1, assuming that defects with trap energy levels are spatially uniformly distributed in the interface, includes: Based on the magnitude of the ferroelectric layer field at time point i, and assuming that defects with trap energy levels are spatially uniformly distributed in the interface, the relative energy difference between the channel conduction band and the defect energy level is calculated. Calculate the charge / discharge barrier based on the relative energy difference; Based on the band shift between the interface layer and the channel and the charge / discharge barrier, the tunneling probability is calculated when the defect with trap energy level is spatially uniformly distributed in the interface. The transition rate between occupied and unoccupied states of a defect with a trap energy level is calculated based on the tunneling probability. Based on the probability that a defect with a trap energy level is in an occupied state at time i, the conversion rate, and the unit time length, calculate the probability that a defect with a trap energy level is in an occupied state at time i+1. Calculate the defect charge at time i+1 based on the probability that a defect with a trap energy level is in an occupied state at time i+1.

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